Joseph Louis Lagrange was an Italian mathmatician and astronomer. He studied at the College of Turin where his favorite subject was classic Latin. Lagrange became very interested in mathematics and astronomy after reading Halley's 1693 work on the use of algebra in optics. Lagrange became self motivated and taught himself since he did not have the opportunities to study with the leading mathematicians. He was the oldest of 11 children and one of 2 who survived to adulthood.He was born in Italy (Turin, Sardinia-Piedmont ) but is considered to be the Italian born French mathematician.
Insight and Influences
Joseph Louis Lagrange, the greatest mathematician of the eighteenth century, was born at Turin on January 25, 1736. His father had charge of the Sardinian military chest. He was of good social position and wealth. Before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely for his position on his own abilities. He was educated at the college of Turin, but it was not until
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he was seventeen that he showed any taste for mathematics. His interest in Mathematics was first excited by a memoir by Edmund Halley which he came across by accident. He threw himself into mathematical studies alone and without any help. At the end of a long and hard working year he was already an accomplished mathematician, and was made a lecturer in the artillery school. Lagrange's interest in mathematics began when he read a copy of Halley's 1693 work on the use of algebra in optics. Physics caught his eye also by the great teachings of Beccaria at the college of Turin. This was when he decided to make a career for himself in mathematics. Perhaps the world of mathematics has to thank Lagrange's father for his unsound financial speculation, for Lagrange later claimed:- If I had been rich, I probably would not have devoted myself to mathematics. He certainly did devote himself to mathematics, but largely he was self taught and did not have the benefit of studying with leading mathematicians. [5]
His best influence was his contribution to the metric system and his addition of the decimal base which is in his place largely due to his plan. Some refer to Lagrange as the founder of the Metric System. The first fruit of Lagrange's labors here was his letter, written around 1854, to famous mathematician Leonhard Euler, in which he solved the isoperimetrical problem which for more than half a century had been a popular subject among mathematicians. What made Lagrange write this letter was a statement by Euler in one of his memoirs leaving the solution of the problem to the "metaphysicians." In 1758, with the help of his classmates, Lagrange established a society, which was incorporated as the Turin Academy. Most of his early writings are to be found in the five volumes of its transactions, usually known as the Miscellanea Taurinensia. Many of these are elaborate papers. His earliest interests were literary rather than scientific, and he earned the basics of geometry during his first year at the college of Turin, without difficulty, but without distinction. Lagrange was very intelligent and learning a subject as common as geometry was a necessity for his career. Lagrange, at the age of nineteen. communicated to others his idea of a general method of working with "isoperimetrical" problems, known later as the Calculus of Variations. It was greatly welcomed by the Berlin mathematician, who had the benevolence to withhold from publication his own further researches on the subject, until his young correspondent should have had time to complete and opportunity to claim the invention[7]
Major Contributions
Joseph Louis Lagrange began working on the tautochrone, and made some important discoveries which would contribute substantially to the new subject of the calculus of variations. After impressing Euler by sending him some results, he was appointed professor of mathematics at the Royal Artillery School in Turin in 1755. In 1756, Lagrange generalized results which Euler had himself obtained in calculus of variations.
In 1756, he was elected to the Berlin Academy. In 1757, Lagrange was a founding member of what would become the Royal Academy of Science of Turin. This new society had major roles to filful including, publishing a scientific journal. Lagrange was a head contributor to the first three volumes.
In 1766, Lagrange accepted Euler's position in the Berlin Academy when Euler left for St. Petersburg. He was greeted well by most members of the Academy, and he soon became close friends with Lambert. Lagrange worked at Berlin for 20 years, producing a numerous amount of top quality papers and regularly winning the prize from the Académie des Sciences of Paris. He shared the 1772 prize on the three body problem with Euler, won the prize for 1774, another one on the motion of the moon, and he won the 1780 prize on perturbations of the orbits of comets by the planets.
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His work in Berlin covered many topics like, astronomy, the stability of the solar system, mechanics, dynamics, fluid mechanics, probability, and the foundations of the calculus. He also worked on number theory, proving in 1770 that every positive integer is the sum of four squares. In 1771, he proved Wilson's theorem, that n is prime if and only if (n-1)! + 1 is divisible by n. In 1770, he also presented an important work which made a fundamental investigation of why equations of degrees up to 4 could be solved by radicals. The paper is the first to consider the roots of a equation as abstract quantities rather than having numerical values. He studied permutations of the roots and, although he does not compose permutations in the paper, it can be considered as a first step in the development of group theory continued by Ruffini, Galois and Cauchy.
Although Lagrange had made numerous major contributions to mechanics, he had not produced a great amount of work. He decided to write a definitive work incorporating his contributions. The Mécanique analytique summarized all the work done in the field of mechanics since the time of Newton, and is notable for its use of the theory of differential equations. With this work Lagrange transformed mechanics into a branch of mathematical analysis. [8] Lagrange made great contributions to many different branches of mathematics. Some of the most important ones are on calculus of variations, solution of polynomial equations and power series and functions. [9]In 1793 he became president of the commission on weights and measures; he was influential in causing the adoption of the decimal base for the metric system. A professor at the École polytechnique from 1797, he developed the use in teaching of the analytic method that he so skillfully employed in his research. His contributions to the development of mathematics also include the application of differential calculus to the theory of probabilities and notable work on the solution of equations. In astronomy he is known for his calculations of the motion.[10] In 1761 Lagrange stood without a rival as the foremost mathematician living; but the unceasing labour of the preceding nine years had seriously affected his health, and the doctors refused to be responsible for his reason or life unless he would take rest and exercise. Although his health was temporarily restored its tone, and henceforth he constantly suffered from attacks of profound melancholy. The next work he produced was in 1764 on the libration of the Moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780.[11] Joseph Louis Lagrange was a major contributist to mathematics, mechanics, and many other pparts of physics.
Affect and Effect
The first affect of Lagrange's labors here was his letter, written when he was still only nineteen, to Euler, in which he solved the isoperimetrical problem which for more than half a century had people talking. To effect the solution (in which he sought to determine the form of a function so that a formula in which it entered should satisfy a certain condition) he enunciated the principles of the calculus of variations. In 1758 Lagrange established with the aid of his pupils a society, which was subsequently incorporated as the Turin Academy, and in the five volumes of its transactions, usually known as the Miscellanea Taurinensia, most of his early writings are to be found. In the volumes it has information about theory and notation of the calculus of variations; and he illustrates its use by deducing the principle of least action, and by solutions of various problems in dynamics. In 1761 Lagrange stood without a rival as the foremost mathematician living; but the unceasing labour of the preceding nine years had seriously affected his health, and the doctors refused to be responsible for his reason or life unless he would take rest and exercise. Although his health was temporarily restored his nervous system never quite recovered its tone, and henceforth he constantly suffered from attacks of profound melancholy. The next work he produced was in 1764 on the libration of the moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780. He now started to go on a visit to London, but on the way fell ill at Paris. There he was received with marked honour, and it was with regret he left the brilliant society of that city to return to his provincial life at Turin. His further stay in Piedmont was, however, short. In 1766 Euler left Berlin, and Frederick the Great immediately wrote expressing the wish of the greatest king in Europe'' to have the greatest mathematician in Europe'' resident at his court. Lagrange accepted the offer and spent the next twenty years in Prussia, where he produced not only the long series of memoirs published in the Berlin and Turin transactions, but his monumental work, the Mecanique analytique. His residence at Berlin commenced with an unfortunate mistake. Finding most of his colleagues married, and assured by their wives that it was the only way to be happy, he married; his wife soon died, but the union was not a happy one. Lagrange was a favourite of the king, who used frequently to discourse to him on the advantages of perfect regularity of life. The lesson went home, and thenceforth Lagrange studied his mind and body as though they were machines, and found by experiment the exact amount of work which he was able to do without breaking down. Every night he set himself a definite task for the next day, and on completing any branch of a subject he wrote a short analysis to see what points in the demonstrations or in the subject-matter were capable of improvement. He always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction. His mental activity during these twenty years was amazing. Not only did he produce his splendid Mécanique analytique, but he contributed between one and two hundred papers to the Academies of Berlin, Turin, and Paris. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time when he was ill he produced on average about one memoir a month. Of these I note the following as amongst the most important.
The Things He Left Behind
Joseph Louis Lagrange accomplished many things and left behind information that is very useful for todays scientists, teachers, astronomers, and doctors. He left behind the "Mecanique Analutique". Which is considered to be his monumental work in the pure maths. Lagrange made many contributions to different branches of mathematics. Joseph Louis Lagrange made some important discoveries that contributed to the new subject of the calculus of variations as well.
Table of Contents
Joseph Louis Lagrange
Joseph Louis Lagrange was an Italian mathmatician and astronomer. He studied at the College of Turin where his favorite subject was classic Latin. Lagrange became very interested in mathematics and astronomy after reading Halley's 1693 work on the use of algebra in optics. Lagrange became self motivated and taught himself since he did not have the opportunities to study with the leading mathematicians. He was the oldest of 11 children and one of 2 who survived to adulthood.He was born in Italy (Turin, Sardinia-Piedmont ) but is considered to be the Italian born French mathematician.
Insight and Influences
Joseph Louis Lagrange, the greatest mathematician of the eighteenth century, was born at Turin on January 25, 1736. His father had charge of the Sardinian military chest. He was of good social position and wealth. Before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely for his position on his own abilities. He was educated at the college of Turin, but it was not until
His best influence was his contribution to the metric system and his addition of the decimal base which is in his place largely due to his plan. Some refer to Lagrange as the founder of the Metric System. The first fruit of Lagrange's labors here was his letter, written around 1854, to famous mathematician Leonhard Euler, in which he solved the isoperimetrical problem which for more than half a century had been a popular subject among mathematicians. What made Lagrange write this letter was a statement by Euler in one of his memoirs leaving the solution of the problem to the "metaphysicians." In 1758, with the help of his classmates, Lagrange established a society, which was incorporated as the Turin Academy. Most of his early writings are to be found in the five volumes of its transactions, usually known as the Miscellanea Taurinensia. Many of these are elaborate papers. His earliest interests were literary rather than scientific, and he earned the basics of geometry during his first year at the college of Turin, without difficulty, but without distinction. Lagrange was very intelligent and learning a subject as common as geometry was a necessity for his career. Lagrange, at the age of nineteen. communicated to others his idea of a general method of working with "isoperimetrical" problems, known later as the Calculus of Variations. It was greatly welcomed by the Berlin mathematician, who had the benevolence to withhold from publication his own further researches on the subject, until his young correspondent should have had time to complete and opportunity to claim the invention[7]
Major Contributions
Joseph Louis Lagrange began working on the tautochrone, and made some important discoveries which would contribute substantially to the new subject of the calculus of variations. After impressing Euler by sending him some results, he was appointed professor of mathematics at the Royal Artillery School in Turin in 1755. In 1756, Lagrange generalized results which Euler had himself obtained in calculus of variations.In 1756, he was elected to the Berlin Academy. In 1757, Lagrange was a founding member of what would become the Royal Academy of Science of Turin. This new society had major roles to filful including, publishing a scientific journal. Lagrange was a head contributor to the first three volumes.
In 1766, Lagrange accepted Euler's position in the Berlin Academy when Euler left for St. Petersburg. He was greeted well by most members of the Academy, and he soon became close friends with Lambert. Lagrange worked at Berlin for 20 years, producing a numerous amount of top quality papers and regularly winning the prize from the Académie des Sciences of Paris. He shared the 1772 prize on the three body problem with Euler, won the prize for 1774, another one on the motion of the moon, and he won the 1780 prize on perturbations of the orbits of comets by the planets.
His work in Berlin covered many topics like, astronomy, the stability of the solar system, mechanics, dynamics, fluid mechanics, probability, and the foundations of the calculus. He also worked on number theory, proving in 1770 that every positive integer is the sum of four squares. In 1771, he proved Wilson's theorem, that n is prime if and only if (n-1)! + 1 is divisible by n. In 1770, he also presented an important work which made a fundamental investigation of why equations of degrees up to 4 could be solved by radicals. The paper is the first to consider the roots of a equation as abstract quantities rather than having numerical values. He studied permutations of the roots and, although he does not compose permutations in the paper, it can be considered as a first step in the development of group theory continued by Ruffini, Galois and Cauchy.
Although Lagrange had made numerous major contributions to mechanics, he had not produced a great amount of work. He decided to write a definitive work incorporating his contributions. The Mécanique analytique summarized all the work done in the field of mechanics since the time of Newton, and is notable for its use of the theory of differential equations. With this work Lagrange transformed mechanics into a branch of mathematical analysis. [8] Lagrange made great contributions to many different branches of mathematics. Some of the most important ones are on calculus of variations, solution of polynomial equations and power series and functions. [9]In 1793 he became president of the commission on weights and measures; he was influential in causing the adoption of the decimal base for the metric system. A professor at the École polytechnique from 1797, he developed the use in teaching of the analytic method that he so skillfully employed in his research. His contributions to the development of mathematics also include the application of differential calculus to the theory of probabilities and notable work on the solution of equations. In astronomy he is known for his calculations of the motion.[10] In 1761 Lagrange stood without a rival as the foremost mathematician living; but the unceasing labour of the preceding nine years had seriously affected his health, and the doctors refused to be responsible for his reason or life unless he would take rest and exercise. Although his health was temporarily restored its tone, and henceforth he constantly suffered from attacks of profound melancholy. The next work he produced was in 1764 on the libration of the Moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780.[11] Joseph Louis Lagrange was a major contributist to mathematics, mechanics, and many other pparts of physics.
Affect and Effect
The first affect of Lagrange's labors here was his letter, written when he was still only nineteen, to Euler, in which he solved the isoperimetrical problem which for more than half a century had people talking. To effect the solution (in which he sought to determine the form of a function so that a formula in which it entered should satisfy a certain condition) he enunciated the principles of the calculus of variations. In 1758 Lagrange established with the aid of his pupils a society, which was subsequently incorporated as the Turin Academy, and in the five volumes of its transactions, usually known as the Miscellanea Taurinensia, most of his early writings are to be found. In the volumes it has information about theory and notation of the calculus of variations; and he illustrates its use by deducing the principle of least action, and by solutions of various problems in dynamics. In 1761 Lagrange stood without a rival as the foremost mathematician living; but the unceasing labour of the preceding nine years had seriously affected his health, and the doctors refused to be responsible for his reason or life unless he would take rest and exercise. Although his health was temporarily restored his nervous system never quite recovered its tone, and henceforth he constantly suffered from attacks of profound melancholy. The next work he produced was in 1764 on the libration of the moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780. He now started to go on a visit to London, but on the way fell ill at Paris. There he was received with marked honour, and it was with regret he left the brilliant society of that city to return to his provincial life at Turin. His further stay in Piedmont was, however, short. In 1766 Euler left Berlin, and Frederick the Great immediately wrote expressing the wish of the greatest king in Europe'' to have the greatest mathematician in Europe'' resident at his court. Lagrange accepted the offer and spent the next twenty years in Prussia, where he produced not only the long series of memoirs published in the Berlin and Turin transactions, but his monumental work, the Mecanique analytique. His residence at Berlin commenced with an unfortunate mistake. Finding most of his colleagues married, and assured by their wives that it was the only way to be happy, he married; his wife soon died, but the union was not a happy one. Lagrange was a favourite of the king, who used frequently to discourse to him on the advantages of perfect regularity of life. The lesson went home, and thenceforth Lagrange studied his mind and body as though they were machines, and found by experiment the exact amount of work which he was able to do without breaking down. Every night he set himself a definite task for the next day, and on completing any branch of a subject he wrote a short analysis to see what points in the demonstrations or in the subject-matter were capable of improvement. He always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction. His mental activity during these twenty years was amazing. Not only did he produce his splendid Mécanique analytique, but he contributed between one and two hundred papers to the Academies of Berlin, Turin, and Paris. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time when he was ill he produced on average about one memoir a month. Of these I note the following as amongst the most important.The Things He Left Behind
Joseph Louis Lagrange accomplished many things and left behind information that is very useful for todays scientists, teachers, astronomers, and doctors. He left behind the "Mecanique Analutique". Which is considered to be his monumental work in the pure maths. Lagrange made many contributions to different branches of mathematics. Joseph Louis Lagrange made some important discoveries that contributed to the new subject of the calculus of variations as well.References